Once you've beaten Spore Spawn, it'll turn to stone and you'll be able to climb up the shaft above. Go through the door at the top and go over to the far end of the next corridor. Drop down through the floor there to fall down a never-ending shaft, once at the bottom you'll find Super Missile no. 1 (Brinstar).
Go left and exit the room. Cross through the next corridor to make your way back to the large purple shaft. Use a Super Missile to break open the wall and crawl through to reach the shaft. Go down to the very bottom of the shaft, then go over to the door in the corner. Use a Super Missile to break it open, then head in to find a green corridor gradually sloping downwards. Go down the corridor, just watch out for the small flying enemies that pop out of the green pipes. Don't forget to grab missile no. 6 (Brinstar) on the way down.
Once you reach the shutter, shoot it open and blast all the Sidehoppers on the other side. Go through the door on the right to find another long green corridor. In here you'll find a large elevated platform leading off down the corridor, but once you reach the point where the spikes are lined along the ceiling the platform blocks will crumble and you'll fall through. To get through here hold down B to dash while you're walking forward, this way Samus will make it across without falling. Head through the door at the end of the corridor to reach a large orange shaft.
Once inside, drop down below and keep falling down past all the Ripper you'll find, eventually you'll reach the bottom. Through the door on the left is an Energy Refill room, once you're ready go through the door on the right. Just above this room is another beam upgrade, the Spazer. Once you've secured it, head through the door on the right side of the room to enter Maridia. Walk through the tunnel underwater and don't worry about exploring, you'll be covering every inch of Maridia later on. Once you re-enter Brinstar you'll find the elevator leading down to Norfair.
Ride the elevator down into the inferno, just remember that Samus' suit won't protect her against hot rooms, so turn back if you begin losing energy. Drop down to the bottom of the shaft containing the main elevator, then go through the door on the left. In here you'll find Energy Tank no. 1 (Norfair), once you get it walk over to the wall to fall through crumbling blocks. Sneak through the narrow tunnels but watch out for the orange Geemer.
Drop down the shaft and head through the door at the bottom to find the Hi-Jump Boots, go back into the large room and jump up the platforms above the door to eventually find missile no. 1 (Norfair). Blast the Geemer, then head back to the main shaft. Leave Norfair, once the elevator takes you back up to Brinstar, blow open the wall on the right with a Super Missile. Head through and jump up to the high platform. Walk past the ugly statue in the foreground, then head through the door there. Proceed through the next few rooms, eventually you'll reach a room full of Keyhunters.
Whack them all, you can then find a Save room on the far right end of the hallway, but once you're ready go to the center of the room and shoot out a section in the floor to reveal another tunnel.
Go down and head through the door there. In the next green corridor the music will change to a warning type tune, so you'll know that your near a main boss. Go through the corridor while blasting the Zebesians there, and watch out for the small thorns that come flying past. At the far end of the corridor you'll face the Kraid Spawn, just whack it with Missiles to finish it off.
In the next room, you can go up through the ceiling above to find a room with an Energy/Missile Refill station, but at the end of the room you'll find a boss guard door (and the remains of a Federation Soldier). Destroy the door when the eye opens then head through to face the first main boss of the game, Kraid. Refer to the bosses guide to send the overgrown lizard packing.